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arXiv · 1909.00487

Finite generation for Hochschild cohomology of Gorenstein monomial algebras

Vladimir Dotsenko·Vincent Gélinas·Pedro Tamaroff
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Abstract

We show that a finite dimensional monomial algebra satisfies the finite generation conditions of Snashall-Solberg for Hochschild cohomology if and only if it is Gorenstein. This gives, in the case of monomial algebras, the converse to a theorem of Erdmann-Holloway-Snashall-Solberg-Taillefer. We also give a necessary and sufficient combinatorial criterion for finite generation.

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Vladimir Dotsenko, Vincent Gélinas, Pedro Tamaroff. 2019-09-01. Finite generation for Hochschild cohomology of Gorenstein monomial algebras. https://doi.org/10.1007/s00029-022-00817-8

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